Express 0.99999...... in the form $straight p over straight q comma$ Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Solution

Let x = 0.99999......
Multiplying both sides by 10 (since one digit is repeating), we get
10x = 9.9999 .........
$rightwards double arrow$ 10x = 9 + 0.99999 ......
$rightwards double arrow$ 10x = 9 + x
$rightwards double arrow$ 10x - x = 9
$rightwards double arrow$ 9x = 9
$rightwards double arrow space$ $x equals 9 over 9 equals 1$
Thus, 0.99999 ....... = 1 = $1 over 1$
Here, p = 1
q = 1
Since 0.99999......goes on for ever, so there is no gap between 1 and 0.99999......and hence they are equal.

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Express 0.99999...... in the form $straight p over straight q comma$ Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

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Express 0.99999...... in the form Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Some More Questions From Polynomials Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Express 0.99999...... in the form $straight p over straight q comma$ Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.